TALK by S. Chatterjee

Souther California Probability Symposium

December 3, 2005

Duality Between Normal Approximation and Concentration Around the Mean

Sourav Chatterjee (UCB)

I will show that, in a very broad sense, every normal approximation problem has a dual problem in concentration; the 'distance from normality' of a given random variable, under very general circumstances, can be measured in terms of the 'deviation from the mean' of some other random variable (the dual problem). Although such a reduction is possible in the presence of a martingale, the current approach bypasses the need for martingales, and gives something more fundamental and wide-ranging. Some illustrative examples will be worked out.